Human physiological(biological)systems function in such a way that their complexity requires mathematical analysis.The functioning of the brain,heart and other parts are so complex to be easily comprehended.Under cond...Human physiological(biological)systems function in such a way that their complexity requires mathematical analysis.The functioning of the brain,heart and other parts are so complex to be easily comprehended.Under conditions of rest or work,the temporal distances of successive heartbeats are subject to fluctuations,thereby forming the basis of Heart Rate Variability(HRV).In normal conditions,the human is persistently exposed to highly changing and dynamic situational demands.With these demands in mind,HRV can,therefore,be considered as the human organism’s ability to cope with and adapt to continuous situational requirements,both physiologically and emotionally.Fast Fourier Transform(FFT)is used in various physiological signal processing,such as heart rate variability.FFT allows a spectral analysis of HRV and is great help in HRV analysis and interpretation.展开更多
A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in t...A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.展开更多
In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a contr...In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a control of complex technical systems, financial mathematics, mathematical biology and medicine. We propose to use a spectral method formalism to the probabilistic analysis problem for the stochastic systems with jumps. This method allows to get a solution of the analysis problem in an explicit form.展开更多
In this paper, we propose extraction of signals correlated with noise in which they are buried. Proposed extraction method uses no a-priori information on the buried signal and works independently of the nature of noi...In this paper, we propose extraction of signals correlated with noise in which they are buried. Proposed extraction method uses no a-priori information on the buried signal and works independently of the nature of noise, correlated or not with the signal, colored or white, Gaussian or not, and locations of its spectral extent. Extraction of buried correlated signals is achieved without averaging in the time or frequency domain.展开更多
In this paper, we propose extraction of signals buried in non-ergodic processes. It is shown that the proposed method extracts signals defined in a non-ergodic framework without averaging or smoothing in the direct ti...In this paper, we propose extraction of signals buried in non-ergodic processes. It is shown that the proposed method extracts signals defined in a non-ergodic framework without averaging or smoothing in the direct time or frequency domain. Extraction is achieved independently of the nature of noise, correlated or not with the signal, colored or white, Gaussian or not, and locations of its spectral extent. Performances of the pro-posed extraction method and comparative results with other methods are demonstrated via experimental Doppler velocimetry measurements.展开更多
Constrained spectral non-negative matrix factorization(NMF)analysis of perturbed oscillatory process control loop variable data is performed for the isolation of multiple plant-wide oscillatory sources.The technique i...Constrained spectral non-negative matrix factorization(NMF)analysis of perturbed oscillatory process control loop variable data is performed for the isolation of multiple plant-wide oscillatory sources.The technique is described and demonstrated by analyzing data from both simulated and real plant data of a chemical process plant. Results show that the proposed approach can map multiple oscillatory sources onto the most appropriate control loops,and has superior performance in terms of reconstruction accuracy and intuitive understanding compared with spectral independent component analysis(ICA).展开更多
Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral...Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral analysis（SPECAN） algorithm is proposed and applied in the BiSAR system.The modifications include Doppler centroid compensation,range curve correction and azimuth processing method.The modified SPECAN algorithm solves the imaging problem under the condition of huge range migration,long synthetic aperture time and phase-coded signal.The proposed algorithm is verified by experiment results.展开更多
A digital ASIC chip customized for battery-operated body sensing devices is presented.The ASIC incorporates a novel hybrid-architecture fast Fourier transform（FFT） unit that is capable of scalable spectral analysis,...A digital ASIC chip customized for battery-operated body sensing devices is presented.The ASIC incorporates a novel hybrid-architecture fast Fourier transform（FFT） unit that is capable of scalable spectral analysis,a licensed ARM7TDMI IP hardcore and several peripheral IP blocks.Extensive experimental results suggest that the complete chip works as intended.The power consumption of the FFT unit is 0.69 mW @ 1 MHz with 1.8 V power supply.The low-power and programmable features of the ASIC make it suitable for＇on-the-fly＇ low-frequency physiological signal processing.展开更多
It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multip...It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise.The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.展开更多
文摘Human physiological(biological)systems function in such a way that their complexity requires mathematical analysis.The functioning of the brain,heart and other parts are so complex to be easily comprehended.Under conditions of rest or work,the temporal distances of successive heartbeats are subject to fluctuations,thereby forming the basis of Heart Rate Variability(HRV).In normal conditions,the human is persistently exposed to highly changing and dynamic situational demands.With these demands in mind,HRV can,therefore,be considered as the human organism’s ability to cope with and adapt to continuous situational requirements,both physiologically and emotionally.Fast Fourier Transform(FFT)is used in various physiological signal processing,such as heart rate variability.FFT allows a spectral analysis of HRV and is great help in HRV analysis and interpretation.
文摘A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.
文摘In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a control of complex technical systems, financial mathematics, mathematical biology and medicine. We propose to use a spectral method formalism to the probabilistic analysis problem for the stochastic systems with jumps. This method allows to get a solution of the analysis problem in an explicit form.
文摘In this paper, we propose extraction of signals correlated with noise in which they are buried. Proposed extraction method uses no a-priori information on the buried signal and works independently of the nature of noise, correlated or not with the signal, colored or white, Gaussian or not, and locations of its spectral extent. Extraction of buried correlated signals is achieved without averaging in the time or frequency domain.
文摘In this paper, we propose extraction of signals buried in non-ergodic processes. It is shown that the proposed method extracts signals defined in a non-ergodic framework without averaging or smoothing in the direct time or frequency domain. Extraction is achieved independently of the nature of noise, correlated or not with the signal, colored or white, Gaussian or not, and locations of its spectral extent. Performances of the pro-posed extraction method and comparative results with other methods are demonstrated via experimental Doppler velocimetry measurements.
基金Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry.
文摘Constrained spectral non-negative matrix factorization(NMF)analysis of perturbed oscillatory process control loop variable data is performed for the isolation of multiple plant-wide oscillatory sources.The technique is described and demonstrated by analyzing data from both simulated and real plant data of a chemical process plant. Results show that the proposed approach can map multiple oscillatory sources onto the most appropriate control loops,and has superior performance in terms of reconstruction accuracy and intuitive understanding compared with spectral independent component analysis(ICA).
基金Sponsored by the National Natural Science Foundation of China(60890071-1160890071-0760890073)
文摘Global navigation satellite system（GNSS） can be employed as a transmitter to composite bistatic synthetic aperture radar（BiSAR）.As GNSS signal is quite different from the traditional radar signal,modified spectral analysis（SPECAN） algorithm is proposed and applied in the BiSAR system.The modifications include Doppler centroid compensation,range curve correction and azimuth processing method.The modified SPECAN algorithm solves the imaging problem under the condition of huge range migration,long synthetic aperture time and phase-coded signal.The proposed algorithm is verified by experiment results.
基金supported by the National Natural Science Foundation of China(Nos.60932001,61072031)the Guangdong Innovation Research Team Fund for Low-Cost Healthcare Technologies+1 种基金the National Basic Research Program of China(No.20 I0CB732606)the 'One-hundred Talent' and the 'Low-Cost Healthcare' Programs of the Chinese Academy of Sciences
文摘A digital ASIC chip customized for battery-operated body sensing devices is presented.The ASIC incorporates a novel hybrid-architecture fast Fourier transform（FFT） unit that is capable of scalable spectral analysis,a licensed ARM7TDMI IP hardcore and several peripheral IP blocks.Extensive experimental results suggest that the complete chip works as intended.The power consumption of the FFT unit is 0.69 mW @ 1 MHz with 1.8 V power supply.The low-power and programmable features of the ASIC make it suitable for＇on-the-fly＇ low-frequency physiological signal processing.
基金financially supported by the Russian Foundation for Basic Research,Project No.17-08-00530.
文摘It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise.The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.
